I'd do a compression check, not only cuz you're mysteriously losing coolant but also cuz you drove the car with the temperature gauge pegged. Aluminum heads don't like getting that hot. A dead give-away for burning coolant is, when you're doing the compression check, the gauge will have drops of water on it when you remove it.

If the cylinders are all good, do a very careful check with a flashlight around the entire cooling system. with the car running and at operating temperature, twist each of the hoses including the heater core hoses. I'd recommend gloves for this. Make sure every hose is seated well, flexes easily, and isn't cracked. You could be losing coolant though a pinhole crack in one of the several tiny hoses that sit behind the engine.